NEW YORK — Donald Trump said Sunday he tapped Reince Priebus — the Republican Party chairman who helped engineer his stunning presidential victory last week — as his White House chief of staff.

Trump also considered campaign CEO Steve Bannon for the slot, but announced that the former Breitbart News executive would serve chief strategist and senior counselor for the administration that takes office in little more than two months.

“I am thrilled to have my very successful team continue with me in leading our country,” Trump said in a statement. “Steve and Reince are highly qualified leaders who worked well together on our campaign and led us to a historic victory. Now I will have them both with me in the White House as we work to make America great again.”

In thanking Trump for the appointment, Priebus said he would strive to "create an economy that works for everyone, secure our borders, repeal and replace Obamacare and destroy radical Islamic terrorism."

Bannon, who began working with Trump over the summer, said that "we had a very successful partnership on the campaign, one that led to victory. We will have that same partnership in working to help President-elect Trump achieve his agenda.”

While planning to move forward soon with staff and policy decisions, Trump also said this weekend that his proposed wall along the U.S.-Mexican border may include some fencing instead and his initial deportation plan will focus on "criminals" who are in the country illegally.

In "certain areas, a wall is more appropriate," but "there could be some fencing," Trump said in an interview with CBS’ Sunday newsmagazine 60 Minutes.

While pledging more deportations, Trump said he would emphasize criminals before deciding what to do about law-abiding families who are in the country illegally.

"What we are going to do is get the people that are criminal and have criminal records, gang members, drug dealers," Trump told CBS, later adding: "After the border is secure and after everything gets normalized, we're going to make a determination on the people that they're talking about who are terrific people."

Trump put the number of deportable criminals at two to three million. but immigration experts say it is much lower.

In addition to the 60 Minutes interview, the president-elect and aides holed up high in Trump Tower throughout the weekend as they pursued staffing decisions and policy planning for an administration that takes office in little more than two months.

Since his surprise election win over Democrat Hillary Clinton on Tuesday night, Trump has granted a couple of select interviews, spoken with Republican officials and foreign leaders — and tweeted, including more pot shots at his media coverage.

"Wow, the @nytimes is losing thousands of subscribers because of their very poor and highly inaccurate coverage of the 'Trump phenomena," Trump tweeted early Sunday.

In the 60 Minutes interview, Trump called social media a key to his victory over Clinton, and said he expects to continue to use Twitter and other social media while in the White House.

"I'm not saying I love it, but it does get the word out," Trump told CBS News. "When you give me a bad story or when you give me an inaccurate story or when somebody other than you (does so) .... I have a method of fighting back."

Trump also pledged to be "very restrained" with social media, saying "the fact that I have such power in terms of numbers with Facebook, Twitter, Instagram, et cetera, I think it helped me win all of these races where they're spending much more money than I spent. And I won."

Social media, Trump said, "has more power than the money they spent, and I think maybe to a certain extent, I proved that."

Trump also seemed to extend olive branches to his critics over the weekend, including possible compromises on his plan to repeal President Obama's health care law.

Trump spoke in terms of keeping provisions that forbid insurance companies from denying coverage to people with pre-existing conditions.

Trump has also said his priorities include a program of road-and-bridge projects ("infrastructure"), de-regulation of financial institutions, and beefing up border against drugs and illegal immigration.

While the Trump campaign has provided little information, foreign governments have confirmed that their leaders spoke with the president-elect. The government of France, for example, said President Francois Hollande spoke with Trump for some 10 minutes Friday about terrorism and Syria.

A Japanese official said Prime Minister Shinzo Abe will be in New York on Thursday to meet with the incoming U.S. President.

As Trump and his team huddled upstairs in his Manhattan tower, thousands of demonstrators massed outside on Fifth Avenue throughout the weekend, protesting what they called his racist and sexist behavior throughout the campaign. Many protesters pointed out that Clinton will likely win the popular vote over Trump.

In a weekend interview with The Wall Street Journal, Trump said he wants to bring the country together after a rancorous campaign.

Asked if he regretted his own aggressive rhetoric, Trump told the Journal: "No, I won."